---
title: 'TOI-2046b: Hot Jupiter Insights'
url: https://www.emergentmind.com/topics/toi-2046b
type: topic
---

# TOI-2046b: Hot Jupiter Insights

TOI-2046b is a transiting hot Jupiter orbiting an F8 star on a 1.497-day orbit. Since its confirmation from *TESS* photometry and radial-velocity follow-up, it has become notable in three connected lines of investigation: the characterization of a very short-period gas giant, the measurement of a nearly null sky-projected but substantially nonzero true stellar obliquity, and the establishment of a multi-year transit-timing baseline that does not support statistically significant transit-timing variations. The published record also contains a revision of the host-star age, from an initially young-system interpretation to a lower limit of at least 700 Myr [2205.01860, 2501.05615, 2509.21551].

## 1. Discovery and fundamental system parameters

TOI-2046b was reported as one of three new hot Jupiters discovered by the *TESS* space mission. In the discovery analysis, it was characterized as a hot Jupiter on a very tight, nearly circular orbit around an F8 V star, with orbital parameters derived from a joint transit-plus-radial-velocity fit. The transit mid-time and orbital period were reported as \(T_0=(2\,457\,792.2767 \pm 0.0023)\,\mathrm{BJD}\) and \(P=(1.4971842 \pm 0.0000033)\,\mathrm{d}\), while the eccentricity was consistent with zero, \(e \equiv 0\). The scaled semi-major axis was \(a/R_* = 4.75^{+0.18}_{-0.17}\), corresponding to \(a \approx 0.027\,\mathrm{AU}\), and the impact parameter was \(b = 0.51^{+0.06}_{-0.07}\) [2205.01860].

The stellar reflex semi-amplitude was measured as \(K = (374.7 \pm 7.8)\,\mathrm{m\,s^{-1}}\). With \(e=0\), the planetary mass was derived as \(M_p = 2.30 \pm 0.28\,M_J\). From the transit depth \(R_p/R_* = 0.1213^{+0.0017}_{-0.0021}\) and the stellar radius, the planetary radius was found to be \(R_p = 1.44 \pm 0.11\,R_J\), yielding a mean density of \(\rho_p \approx 1.04\,\mathrm{g\,cm^{-3}}\). Under the usual assumption of zero albedo and full redistribution, the equilibrium temperature was estimated as \(T_{\rm eq} \approx 2040\,\mathrm{K}\). These parameters place TOI-2046b among highly irradiated, inflated short-period gas giants.

## 2. Host-star characterization and the age revision

The host star was initially characterized spectroscopically and through spectral-energy-distribution fitting as an F8 V star with \(T_{\rm eff}=6250 \pm 140\,\mathrm{K}\), \(\log g = 4.30 \pm 0.15\) (cgs), \([\mathrm{Fe/H}] = -0.06 \pm 0.15\) dex, and \(v\sin i = 9.8 \pm 1.6\,\mathrm{km\,s^{-1}}\). The spectral-energy-distribution analysis with ARIADNE, incorporating Gaia EDR3 parallax, yielded \(M_* = 1.153^{+0.100}_{-0.093}\,M_\odot\), \(R_* = 1.237^{+0.036}_{-0.032}\,R_\odot\), and an age of \(0.45^{+0.43}_{-0.02}\,\mathrm{Gyr}\). A strong lithium line with \(\mathrm{EW}=0.083 \pm 0.010\,\AA\) and a stable photometric rotation signal at \(3.97 \pm 0.02\,\mathrm{d}\) were taken to argue for a stellar age of \(100\)–\(400\,\mathrm{Myr}\) [2205.01860, 2501.05615].

A later HARPS-N-based analysis revised this picture. By stacking all HARPS-N spectra and searching for the Li \(\lambda\,6708\,\AA\) doublet, no Li absorption was detected. Using empirical Li-depletion models, that non-detection in an F8 star was interpreted as placing a firm lower limit of \(\gtrsim 700\,\mathrm{Myr}\) on the stellar age. Independent age indicators were consistent with this revision: the chromospheric activity level was reported as \(\log R'_{HK} = -4.66\), and gyro-age relations yielded ages of \(\sim 0.5\)–\(1.6\,\mathrm{Gyr}\). The current published constraint is therefore that TOI-2046 A is at least \(700\,\mathrm{Myr}\) old. This substantially revises the original classification of the system as very young.

## 3. Spin-orbit geometry and obliquity

The projected stellar obliquity of TOI-2046b was measured from the Rossiter-McLaughlin effect using archival HARPS and HARPS-N spectroscopy. For TOI-2046b specifically, transit observations with HARPS-N at the 3.58-m TNG on 2022-09-29/30 produced 31 spectra, including 13 in transit, with 600 s exposures and per-exposure \(S/N \simeq 15\)–26 at 550 nm. The data were reduced with the standard HARPS Data Reduction Software, which provides barycentric 1D spectra and cross-correlation functions whose centroids yield the instantaneous radial velocity and whose line profiles encode the Rossiter-McLaughlin anomaly. The anomaly was modeled with ARoMEpy, combining a Keplerian orbit from RadVel, a CCF-based analytic Rossiter-McLaughlin anomaly through the Boué model, quadratic limb darkening from ATLAS9 with Gaussian priors, Gaussian priors on the systemic velocity \(\Gamma\) and semi-amplitude \(K\), and uniform priors on \(v\sin i_*\) and \(\lambda \in [-180^\circ,+180^\circ]\). Three independent MCMC runs of \(20\) walkers \(\times\) \(12\,500\) steps, with a \(2\,500\)-step burn-in, were required to satisfy \(\mathrm{Gelman\text{-}Rubin}<1.001\) [2501.05615].

This analysis yielded a sky-projected obliquity of
\[
\lambda = 1^\circ \pm 6^\circ .
\]
Taken in isolation, this result is consistent with an aligned projected geometry. However, the same study derived the stellar rotation period from *TESS* photometry as \(P_{\rm rot} = 4.05 \pm 0.05\,\mathrm{d}\) through a Lomb-Scargle periodogram of the long-cadence light curve. Combining \(P_{\rm rot}\) with the spectroscopic \(v\sin i_* = 8.9^{+1.3}_{-1.2}\,\mathrm{km\,s^{-1}}\), \(R_* = 1.21 \pm 0.07\,R_\odot\), and the orbital inclination \(i \simeq 83.6^\circ \pm 0.9^\circ\), the true obliquity was inferred from
\[
\cos\psi \;=\;\sin i_*\,\sin i \,\cos|\lambda|\;+\;\cos i_*\,\cos i,
\]
giving
\[
\psi = 42^{+10}_{-8}\,\mathrm{deg}.
\]

TOI-2046b therefore illustrates a recurrent geometric point in obliquity studies: a nearly zero \(\lambda\) does not imply a truly aligned system. In this case, the sky projection is nearly aligned, whereas the three-dimensional spin-orbit angle is moderate and clearly nonzero.

## 4. Transit ephemeris and timing analysis

A later timing study combined the literature epoch \(E=0\) from Kabáth et al. 2022, all *TESS* mid-transit times from sectors 58, 59, 78, and 79, 13 new ADYU60 transits obtained from October 2020 to November 2024, and three TUG-T100 transits obtained from December 2021 to August 2023. These data were combined in a joint linear fit of the form
\[
T_C(E)\;=\;T_0 \;+\;E\,P .
\]
The resulting updated linear ephemeris was
\[
T_0 = 2457792.2753 \pm 0.0002\ \mathrm{BJD}_{\rm TDB},
\]
\[
P   = 1.49718644 \pm 1.5\times10^{-7}\ \mathrm{days},
\]
or, equivalently,
\[
T_C(E) \;=\; 2457792.2753(2)\;+\;E\;\times\;1.49718644(15)\quad\mathrm{[d]}.
\]
The observational basis for this refinement comprised *TESS* 2-min cadence data in sectors 58, 59, 78, and 79, 13 R-band ADYU60 transits, and 3 R/V-band TUG-T100 transits [2509.21551].

Transit-timing variations were then tested against three models. The constant-period model was
\[
t_{\rm tra}(E) = t_0 + P_0\,E .
\]
The orbital-decay model was
\[
t_{\rm tra}(E) = t_0 + P_0\,E + \tfrac12\,\frac{dP}{dE}\,E^2 ,
\]
with fitted
\[
\frac{dP}{dE} = (+1.71\pm2.08)\times10^{-9}\ \mathrm{days\ per\ epoch}.
\]
The apsidal-precession model was
\[
t_{\rm tra}(E) = t_0 + P_s\,E \;-\;\frac{e\,P_a}{\pi}\cos\omega(E),
\]
\[
\omega(E) = \omega_0 + \frac{d\omega}{dE}\,E,\quad
P_s = P_a\Bigl(1-\frac{d\omega/dE}{2\pi}\Bigr).
\]

Model comparison through the Bayesian Information Criterion gave the following results: for the constant-period model, \(k=2\), \(n=74\), \(\chi^2=446.9\), \(\mathrm{BIC}=456.3\), \(\Delta\mathrm{BIC}=0.0\), interpreted as “Best”; for orbital decay, \(k=3\), \(n=74\), \(\chi^2=446.3\), \(\mathrm{BIC}=460.4\), \(\Delta\mathrm{BIC}=4.1\), interpreted as “Positive evidence against”; and for apsidal precession, \(k=5\), \(n=74\), \(\chi^2=449.1\), \(\mathrm{BIC}=472.7\), \(\Delta\mathrm{BIC}=16.4\), interpreted as “Very strong reject.” The lowest BIC therefore belongs to the constant-period model, and the published conclusion is that TOI-2046b shows no statistically significant long-term TTV trend.

## 5. Periodogram results, non-detections, and dynamical constraints

A Generalized Lomb-Scargle periodogram of the observed-minus-calculated residuals returned a peak frequency of \(0.0075\pm0.0001\,\mathrm{Hz}\), corresponding to a period of \(\simeq 132.97\pm2.28\,\mathrm{d}\), with amplitude \(0.0007\pm0.0001\,\mathrm{days}\) and false alarm probability \(\mathrm{FAP}=0.0196\). Because \(0.01 < \mathrm{FAP} < 0.1\), the timing study treated this signal as consistent with background noise and did not claim any periodic TTV [2509.21551].

The same study translated the quadratic timing term into a secular period-derivative constraint. The fitted decay-model coefficient,
\[
\frac{dP}{dE}=(+1.7\pm2.1)\times10^{-9}\ \mathrm{d/epoch},
\]
corresponds to
\[
\dot P = (1.7\times10^{-9}/1.4972)\,{\rm d/d} \simeq 4.2\times10^{-7}\ \mathrm{d/yr} \lesssim 0.04\ \mathrm{s\ yr^{-1}}.
\]
An attempted tidal-quality-factor estimate yielded an unphysical negative value, \(Q\approx -3.4\times10^2\), which was taken as confirmation that no decay is detected. The published interpretation is that the absence of coherent TTVs argues against any nearby undetected perturber or rapid tidal evolution, and that the orbit appears stable on multi-year timescales.

## 6. Formation, migration, and observational significance

The interpretive status of TOI-2046b is shaped by the combination of its short period, high irradiation, inflated radius, obliquity measurements, and timing non-detections. The discovery paper emphasized the system as a test case for hot-Jupiter inflation and orbital evolution, noting the inflated radius \(R_p=1.44\,R_J\), irradiation \(F \gtrsim 10^9\,\mathrm{erg\,s^{-1}\,cm^{-2}}\), and an apparent mismatch between stellar and orbital inclinations, summarized there as \(i_\star \approx 39^\circ\) versus \(i_{\rm orb} = 83.6^\circ\). It also highlighted future observational prospects including atmospheric characterization with JWST, with a transmission signal of \(\sim 330\,\mathrm{ppm}\) [2205.01860, 2501.05615, 2509.21551].

The later obliquity study sharpened the migration discussion. For stars with convective envelopes, the convective-envelope alignment timescale was written as
\[
\tau_{\rm CE} \;\approx\;10^{10}\,\mathrm{yr}\;
\biggl(\frac{M_p}{M_*}\biggr)^{-2}
\bigl(\tfrac{a/R_*}{40}\bigr)^6,
\]
and for TOI-2046b this gives \(\tau_{\rm CE} \simeq 5\times10^{10}\,\mathrm{yr} \gg \mathrm{age}\). On that basis, the measured obliquity is not expected to have been erased by tidal realignment. The study further argued that \(\lambda \approx 0^\circ\) but \(\psi \approx 42^\circ\) is difficult to reconcile with smooth disk migration alone, while classic Kozai-Lidov migration would require a massive inclined companion and none is detected, although a distant or low-mass perturber cannot be ruled out. A stated alternative is primordial disk-star misalignment. When combined with the timing result that no statistically significant TTVs are present, the current picture is of a hot Jupiter on a stable multi-year orbit whose three-dimensional spin-orbit geometry retains information about formation or early dynamical evolution. Continued high-precision monitoring with the *TESS* extended mission, CHEOPS, and ground-based R-band photometry has been recommended to tighten limits on \(\dot P\) to the cm yr\(^{-1}\) level and to search for very low-amplitude TTVs, while future companion searches and high-precision astrometry such as Gaia DR4 can test whether an unseen perturber contributed to the observed misalignment.

Source: https://www.emergentmind.com/topics/toi-2046b